- Email: [email protected]
Experimental Apparatus for Characterizing the Internal Diffusivity of Microporous Powders
CHINESE JOURNAL OF CATALYSIS Volume 29, Issue 11, November 2008 Online English edition of the Chinese language journal Cite this article as: Chin J Catal, 2008, 29(11): 1133–1137.
RESEARCH PAPER
Experimental Apparatus for Characterizing the Internal Diffusivity of Microporous Powders SONG Zhejian, WANG Dezheng* Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
Abstract: The characterization of the micropore range in porous powders requires sophisticated apparatuses, which limits their thorough characterization to large laboratories. We describe a modification of a BET adsorption apparatus, in which the key instrument is a high precision differential pressure sensor, which even small laboratories can afford, that can be used to measure the internal diffusivity and micropore size distribution (mPSD) of microporous powders. The apparatus is based on the conventional gas uptake rate measurement and adsorption manometry for measuring diffusivity and mPSD, respectively. Numerical simulations of the measurement and uptake rate were used to analyze the apparatus. Key words: microporous powder; diffusivity; micropore size distribution
The practical importance of microporous powders, especially zeolites, has brought with it the problem of characterizing the micropores of these materials. For example, a knowledge of the different diffusivities of different sorbates in porous materials gives chances to use these materials for separations and to control product selectivity in heterogeneous catalysis [1,2]. Both microscopic and macroscopic methods and transient and steady-state measurements, including permeability, Wilke-Kallenbach, time lag, sorption rate measurement, efficiency factor, frequency response, chromatographic methods, pulsed-field gradient (PFG) NMR, and quasielastic neutron scattering, have been used to measure powder internal diffusivities [3]. However, many of the techniques require large crystals and sophisticated apparatuses, which limits the thorough characterization of microporous powders to large laboratories. We describe an apparatus that differs from conventional adsorption instruments only in that it uses a high vacuum leak valve and precision differential pressure transducers, which small laboratories can afford. The apparatus can measure the internal diffusivity and micropore size distribution of microporous powders or high-resolution (closely spaced data points) adsorption isotherms of conventional porous powders. The basis of the micropore size distribution measurement is conventional adsorption manometry as previously reported [4].
This study is an extension of the use of the apparatus to the measurement of internal diffusivity.
1 Experimental 1.1 Theoretical model and analytical method The diffusivity measurement is based on the conventional uptake rate diffusivity measurement [1]. It uses Eq. (1), which is a diffusion equation for gas diffusion inside a porous spherical particle (powders with other geometric shapes can be analyzed by appropriate corresponding changes of the diffusion equation) with radius rp:
§ w 2 q 2 wq · ¸ Dc ¨¨ 2 r wr ¸¹ © wr t < 0, C = 0; r , q = 0 wq wt
(1)
t = 0, C = C; q(rp, t) = K·C
t , r
rp , q (rp , t )
K Cf ; r
0,
Gq Gr
0
where C is the concentration in the gas phase and q is the concentration in the powder particle. The initial condition is that at t < 0, the sample tube and the sample are evacuated and the concentration is zero. At time t = 0, the sample tube is filled with the diffusing gas to a pressure C, which sets the boundary
Received date: 24 September 2008. * Corresponding author. Tel: +86-10-62781469; Fax: +86-10-62772051; E-mail: [email protected] Foundation item: Supported by the National Basic Research Program of China (2005CB221405) and the National Natural Science Foundation of China (20773075). Copyright © 2008, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. Published by Elsevier BV. All rights reserved.
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
condition at r = rp, the outer perimeter of the particle. At r = rp, the concentration is KC (K is Henry's Law constant or the adsorption equilibrium constant). This assumes that there is no external transport limitation so that there is gas-surface concentration equilibrium at the outer perimeter of the particle. This assumption is sometimes questionable with a conventional apparatus for uptake rate measurements of the diffusivity [1]. In our apparatus, the pressure used in the sample cell is of the order of torrs (1 torr = 133 Pa), which is a much lower pressure, and the external transport resistance is much less. The boundary condition at r = 0 is the symmetry condition. In a conventional apparatus for uptake rate measurements of the diffusivity [1], classical analytic solutions of the diffusion equation are used in a least squares optimization to get the best parameter fit for Dc in Eq. (1). A minor difference from this in the work here is that instead of using analytic solutions for the diffusion equation, numerical solutions are used. There are two advantages to doing this. First, Eq. (1) can be easily modified to further include a more complex diffusivity model, e.g., one comprising mesopore diffusion or/and activated surface diffusion that can be expected to be present in an intrawall biporous structure of hybrid structures. Second, and more important for an economical apparatus, because a numerical solution is used, there is no strict requirement to maintain a stable and constant pressure in the sample cell, which would require a sophisticated automatic pressure controller. In our apparatus, an approximately constant pressure is used and can be accurately measured. The measured pressure, 0.3% of the reading precision, is used as the boundary condition at r = rp in Eq. (1). The disadvantage that the computation of the numerical solution is much slower than the analytic solution is negligible nowadays because of the adequate speed of personal computers. In our apparatus, we use hand control of a leak valve to get an approximately constant pressure in the sample tube and can control it such that a deviation less than 3% can be easily obtained. Simulations showed that provided the pressure is measured accurately, the pressure deviation does not affect the accuracy of the diffusivity measurement. 1.2 Apparatus features The main improvement in our apparatus over the conventional uptake rate apparatus is an added key feature that gives the capability to supply and measure very low flow rates. Fig. 1 shows the apparatus, which can provide flow rates that can be lower than 0.01 ml/min. This is a very low range where mass flow controllers and critical flow orifices do not work well. Our apparatus makes use of the measured pressure change in a gas supply burette (of known volume and temperature) to measure the flow rate. There have been previously developed apparatuses that use the pressure change in a gas burette to measure the flow rate, but these measure the pressures in the burette at subsequent times and take the difference to produce the
Fig.1.Schematic of the apparatus.
“measured” pressure change. These cannot be used to make diffusivity measurements due to the limit in precision of 0.1% of the reading for pressure transducers. This is because the inaccuracy of calculating a tiny quantity by subtraction using two much larger numbers requires the use of a very small volume dosing burette, which cannot maintain the constant pressure in the sample cell needed for uptake rate diffusivity measurements. Thus, uptake rate diffusivity measurements have had to use the gravimetric method, but a good vacuum microbalance is expensive [5]. This has led to the alternative of developing the zero length column [6] and frequency response methods, but the experimental protocols for accurate measurements with these can be demanding [1,7]. Our apparatus uses precision pressure differential transducers for directly measuring (as opposed to the indirect method of using subtraction) the pressure change in the gas supply burette (for example, the data in Fig. 2). The differential pressure sensors (No. 5 in Fig. 1, MKS Baratrons Type 22544, which is a modified Type 223B), 10 torr and 1000 torr full scale, are placed between the gas supply burette and a reference gas chamber with gas amount maintained constant. The important feature is that the pressure differential transducers are chosen to be a type that has a precision of 0.3% of reading (in contrast to a constant precision of a fraction of full scale, which cannot measure small differentials precisely). Thus, very small pressure changes in the gas supply burette can be directly measured. The high precision pressure difference measurement allows the use of a large gas supply burette that can supply the (approximately) constant pressure in the sample cell needed for uptake rate diffusivity measurements. A high vacuum leak valve (No. 6 in Fig. 1 from Shenyang Scientific Factory, Type CW16) is used to supply the very low flow rates. This is controlled manually to maintain the pressure in the sample cell approximately constant. An important advantage over many other macroscopic methods for measuring diffusivity is that the flow rate can be low enough to work at a low pressure < 50 torr (6666 Pa), where there is much less adsorption, which avoids
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
the heat evolved (nonisothermality) problem. For samples with a large Henry constant, the working pressure in the sample tube can be < 1 torr (133 Pa).
2 Results and discussion
Table1Comparison of our results for methane diffusivity in ZSM-5 with literature values Methane diffusivity (m2/s) Molecular dynamics simulation
8.68×109 (300 K) [9] Experimental data
Fig. 2 shows the pressure change in the gas supply burette due to different samples with the diffusing gas methane. The ZSM-5 zeolite was a commercial catalyst purchased from Nankai University Catalyst Company. The Al2O3 sample was a commercial powder Type 13-2525 purchased from Strem Chemicals Co. (USA). The experiments were performed at 20 °C. Small temperature differences between the gas supply burette and sample cell and gas supply burette and gas reservoir were measured by differential thermocouples that use the gas supply burette and gas reservoir as the reference junction, respectively. The temperature of the gas reservoir was measured by a thermocouple with an ice-water mixture reference junction. The ideal gas law was used to adjust for pressure changes due to temperature fluctuations. Qualitatively, without any calculations, it can be seen that diffusion is faster in the Al2O3 sample than the HZSM-5 sample. This is seen from that the pressure changes occurred over a shorter time period and reached the steady state faster. From the independent measurement, it is known that the average pore size of the Al2O3 sample is 7 nm, while that of the HZSM-5 sample is 0.5 nm. It can be seen that the apparatus gives results that are qualitatively correct. The quantitative measurement of the diffusivity was performed by the optimization of the parameter Dc in Eq. (1) using a visual comparison, that is, by looking at the computed curves corresponding to different values of Dc and deciding which one is nearest to the experimental curve. The pressure change versus time data reflect the diffusion times in the samples. By solving Eq. (1), we get the solutions and hence the diffusion times for different values of
Fig.2.Pressure change in the gas supply burette due to different samples.
1.26×108 (298 K) [8] 1.05×108 (298 K) [10] 7.0×109 (298 K) [1]
This work
2.0×109–4.3×109 (293 K)
diffusivity. These are then used to get the best match with the experimental data. The results are given in Table 1 and show that our apparatus can be used to measure diffusivities that are in the range shown in Table 1. An experimental difficulty is that there is a finite time interval at the beginning of the measurement when leak valve 6 is first opened. It was found experimentally that it takes about 10 s to get to and maintain a fairly constant final sample cell pressure. In Fig. 2, this 10 interval is the sharp increase in ǻp at the beginning left end of the curve. During this interval, much more of the (negative) ǻp in the gas supply burette is due to the supply of gas to increase the pressure in the sample cell (from zero pressure). In this region, since only a small fraction of ǻp is due to gas diffusing into the powder sample, diffusion data cannot be extracted and are “lost”. In the matching of simulation results and data, it is only data after t = 10 s that can be used. This places a limit on the magnitude of diffusivity that can be measured by the technique because this has to be sufficiently small or the particle made sufficiently large to give a diffusion time that should be > 50 s. This puts an upper measureable limit on the internal diffusivity of about 1×109 m2/s, with some possibility of going a little bit higher if larger particles are available. Fig. 3 shows a Monte Carlo (MC) simulation result that was optimized to match the experimental data from the methane-ZSM-5 diffusion experiment above. The MC simulation parameters include measurement uncertainties that were set as ± 0.5 °C for the temperatures of the gas supply burette, gas reservoir, and sample cell; ± 0.3% of the reading of the differential pressure of Baratron 5 (Fig. 1) if the reading was >0.2 torr, and ± 0.3% of 0.2 torr if the reading was 0.2 torr; ± 0.3% of the reading of the pressure of Baratron 9 (Fig. 1). The pressure in the sample cell was allowed to fluctuate within ± 3% of the pressure. After verifying that the MC simulation can fit the data, further simulations were carried out to seek ways to improve the apparatus. The simulation informs us that modifications should be made to the apparatus that can then allow measurements with a diffusing gas with a small Henry constant (K = 1) to be made. These modifications would use a smaller gas supply burette or/and a smaller sample cell, and the use of a 1 torr full scale Baratron. Also, the experiment should be planned with a slightly higher pressure in the gas supply burette than the pressure in the gas reservoir such that the ǻp of the gas
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
to the presence of micropores.
3 Conclusions The use of high precision differential pressure sensors provides a means to measure the internal diffusivity of microporous powders in a modified BET adsorption apparatus. This apparatus is cheap enough for even quite small laboratories.
References [1] Kärger J, Ruthven D M. Diffusion in Zeolites and Other Microporous Solids. Weinheim: Wiley, 1992. 1 [2] Kärger J, Ruthven D M. In: Schuth F, Sing K S W, Weitkamp J eds. Handbook of Porous Solids, Volume 4. Weinheim: WileyFig.3.Diffusion of CH4 in HZSM-5.
supply burette is close to zero for the experimental data used for parameter fitting. In working with microporous powders, e.g., as in measuring internal diffusivity here, a basic requirement of the apparatus is that it must be able to degas the very narrow pores. This is made possible in the present apparatus by the highly accurate measurement of the pressure and differential pressure changes. These have enough precision to allow the use of a large dead volume in the sample tube. This is necessary for working at very low pressures because a high pumping speed in the sample cell is required. Our apparatus ensures adequate pumping speed at the sample by using large tubings (8 mm inner diameter) to provide a fairly high conductance pumping path (hence, a large dead volume). In many apparatuses, the need to have a small dead volume requires the use of capillary tubings that limit the path conductance. These cannot give a high pumping speed at the sample that needs to be outgassed at very low pressures due
VCH, 2002. 2089 [3] Conner W C, Fraissard J. Fluid Transport in Nanoporous Materials. Heidelberg: Springer, 2006. 151 [4] Li W J, Wang Y, Wang D Zh, Wei F. Chin J Catal, 2006, 27(3): 200 [5] O’Sullivan C K, Guilbault G G. Biosens Bioelectron, 1999, 14(8–9): 663 [6] Qiao S Z, Bhatia S K. Microporous Mesoporous Mater, 2005, 86(1–3): 112 [7] Schuring D. Diffusion in Zeolites: Towards a Microscopic Understanding. Eindhoven: Eindhoven University of Technology, 2002. 13 [8] Goodbody S J, Watanabe K, MacGowan D, Walton J P R B, Quirke N. J Chem Soc, Faraday Trans, 1991, 87(13): 1951 [9] Keil F J, Hinderer J, Garayhi A R. Catal Today, 1999, 50(3–4): 637 [10] Caro J, Bulow M, Schirmer W, Kärger J, Heink W, Pfeifer H, Zdanov S P. J Chem Soc, Faraday Trans, 1985, 81(10): 2541
RESEARCH PAPER
Experimental Apparatus for Characterizing the Internal Diffusivity of Microporous Powders SONG Zhejian, WANG Dezheng* Department of Chemical Engineering, Tsinghua University, Beijing 100084, China
Abstract: The characterization of the micropore range in porous powders requires sophisticated apparatuses, which limits their thorough characterization to large laboratories. We describe a modification of a BET adsorption apparatus, in which the key instrument is a high precision differential pressure sensor, which even small laboratories can afford, that can be used to measure the internal diffusivity and micropore size distribution (mPSD) of microporous powders. The apparatus is based on the conventional gas uptake rate measurement and adsorption manometry for measuring diffusivity and mPSD, respectively. Numerical simulations of the measurement and uptake rate were used to analyze the apparatus. Key words: microporous powder; diffusivity; micropore size distribution
The practical importance of microporous powders, especially zeolites, has brought with it the problem of characterizing the micropores of these materials. For example, a knowledge of the different diffusivities of different sorbates in porous materials gives chances to use these materials for separations and to control product selectivity in heterogeneous catalysis [1,2]. Both microscopic and macroscopic methods and transient and steady-state measurements, including permeability, Wilke-Kallenbach, time lag, sorption rate measurement, efficiency factor, frequency response, chromatographic methods, pulsed-field gradient (PFG) NMR, and quasielastic neutron scattering, have been used to measure powder internal diffusivities [3]. However, many of the techniques require large crystals and sophisticated apparatuses, which limits the thorough characterization of microporous powders to large laboratories. We describe an apparatus that differs from conventional adsorption instruments only in that it uses a high vacuum leak valve and precision differential pressure transducers, which small laboratories can afford. The apparatus can measure the internal diffusivity and micropore size distribution of microporous powders or high-resolution (closely spaced data points) adsorption isotherms of conventional porous powders. The basis of the micropore size distribution measurement is conventional adsorption manometry as previously reported [4].
This study is an extension of the use of the apparatus to the measurement of internal diffusivity.
1 Experimental 1.1 Theoretical model and analytical method The diffusivity measurement is based on the conventional uptake rate diffusivity measurement [1]. It uses Eq. (1), which is a diffusion equation for gas diffusion inside a porous spherical particle (powders with other geometric shapes can be analyzed by appropriate corresponding changes of the diffusion equation) with radius rp:
§ w 2 q 2 wq · ¸ Dc ¨¨ 2 r wr ¸¹ © wr t < 0, C = 0; r , q = 0 wq wt
(1)
t = 0, C = C; q(rp, t) = K·C
t , r
rp , q (rp , t )
K Cf ; r
0,
Gq Gr
0
where C is the concentration in the gas phase and q is the concentration in the powder particle. The initial condition is that at t < 0, the sample tube and the sample are evacuated and the concentration is zero. At time t = 0, the sample tube is filled with the diffusing gas to a pressure C, which sets the boundary
Received date: 24 September 2008. * Corresponding author. Tel: +86-10-62781469; Fax: +86-10-62772051; E-mail: [email protected] Foundation item: Supported by the National Basic Research Program of China (2005CB221405) and the National Natural Science Foundation of China (20773075). Copyright © 2008, Dalian Institute of Chemical Physics, Chinese Academy of Sciences. Published by Elsevier BV. All rights reserved.
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
condition at r = rp, the outer perimeter of the particle. At r = rp, the concentration is KC (K is Henry's Law constant or the adsorption equilibrium constant). This assumes that there is no external transport limitation so that there is gas-surface concentration equilibrium at the outer perimeter of the particle. This assumption is sometimes questionable with a conventional apparatus for uptake rate measurements of the diffusivity [1]. In our apparatus, the pressure used in the sample cell is of the order of torrs (1 torr = 133 Pa), which is a much lower pressure, and the external transport resistance is much less. The boundary condition at r = 0 is the symmetry condition. In a conventional apparatus for uptake rate measurements of the diffusivity [1], classical analytic solutions of the diffusion equation are used in a least squares optimization to get the best parameter fit for Dc in Eq. (1). A minor difference from this in the work here is that instead of using analytic solutions for the diffusion equation, numerical solutions are used. There are two advantages to doing this. First, Eq. (1) can be easily modified to further include a more complex diffusivity model, e.g., one comprising mesopore diffusion or/and activated surface diffusion that can be expected to be present in an intrawall biporous structure of hybrid structures. Second, and more important for an economical apparatus, because a numerical solution is used, there is no strict requirement to maintain a stable and constant pressure in the sample cell, which would require a sophisticated automatic pressure controller. In our apparatus, an approximately constant pressure is used and can be accurately measured. The measured pressure, 0.3% of the reading precision, is used as the boundary condition at r = rp in Eq. (1). The disadvantage that the computation of the numerical solution is much slower than the analytic solution is negligible nowadays because of the adequate speed of personal computers. In our apparatus, we use hand control of a leak valve to get an approximately constant pressure in the sample tube and can control it such that a deviation less than 3% can be easily obtained. Simulations showed that provided the pressure is measured accurately, the pressure deviation does not affect the accuracy of the diffusivity measurement. 1.2 Apparatus features The main improvement in our apparatus over the conventional uptake rate apparatus is an added key feature that gives the capability to supply and measure very low flow rates. Fig. 1 shows the apparatus, which can provide flow rates that can be lower than 0.01 ml/min. This is a very low range where mass flow controllers and critical flow orifices do not work well. Our apparatus makes use of the measured pressure change in a gas supply burette (of known volume and temperature) to measure the flow rate. There have been previously developed apparatuses that use the pressure change in a gas burette to measure the flow rate, but these measure the pressures in the burette at subsequent times and take the difference to produce the
Fig.1.Schematic of the apparatus.
“measured” pressure change. These cannot be used to make diffusivity measurements due to the limit in precision of 0.1% of the reading for pressure transducers. This is because the inaccuracy of calculating a tiny quantity by subtraction using two much larger numbers requires the use of a very small volume dosing burette, which cannot maintain the constant pressure in the sample cell needed for uptake rate diffusivity measurements. Thus, uptake rate diffusivity measurements have had to use the gravimetric method, but a good vacuum microbalance is expensive [5]. This has led to the alternative of developing the zero length column [6] and frequency response methods, but the experimental protocols for accurate measurements with these can be demanding [1,7]. Our apparatus uses precision pressure differential transducers for directly measuring (as opposed to the indirect method of using subtraction) the pressure change in the gas supply burette (for example, the data in Fig. 2). The differential pressure sensors (No. 5 in Fig. 1, MKS Baratrons Type 22544, which is a modified Type 223B), 10 torr and 1000 torr full scale, are placed between the gas supply burette and a reference gas chamber with gas amount maintained constant. The important feature is that the pressure differential transducers are chosen to be a type that has a precision of 0.3% of reading (in contrast to a constant precision of a fraction of full scale, which cannot measure small differentials precisely). Thus, very small pressure changes in the gas supply burette can be directly measured. The high precision pressure difference measurement allows the use of a large gas supply burette that can supply the (approximately) constant pressure in the sample cell needed for uptake rate diffusivity measurements. A high vacuum leak valve (No. 6 in Fig. 1 from Shenyang Scientific Factory, Type CW16) is used to supply the very low flow rates. This is controlled manually to maintain the pressure in the sample cell approximately constant. An important advantage over many other macroscopic methods for measuring diffusivity is that the flow rate can be low enough to work at a low pressure < 50 torr (6666 Pa), where there is much less adsorption, which avoids
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
the heat evolved (nonisothermality) problem. For samples with a large Henry constant, the working pressure in the sample tube can be < 1 torr (133 Pa).
2 Results and discussion
Table1Comparison of our results for methane diffusivity in ZSM-5 with literature values Methane diffusivity (m2/s) Molecular dynamics simulation
8.68×109 (300 K) [9] Experimental data
Fig. 2 shows the pressure change in the gas supply burette due to different samples with the diffusing gas methane. The ZSM-5 zeolite was a commercial catalyst purchased from Nankai University Catalyst Company. The Al2O3 sample was a commercial powder Type 13-2525 purchased from Strem Chemicals Co. (USA). The experiments were performed at 20 °C. Small temperature differences between the gas supply burette and sample cell and gas supply burette and gas reservoir were measured by differential thermocouples that use the gas supply burette and gas reservoir as the reference junction, respectively. The temperature of the gas reservoir was measured by a thermocouple with an ice-water mixture reference junction. The ideal gas law was used to adjust for pressure changes due to temperature fluctuations. Qualitatively, without any calculations, it can be seen that diffusion is faster in the Al2O3 sample than the HZSM-5 sample. This is seen from that the pressure changes occurred over a shorter time period and reached the steady state faster. From the independent measurement, it is known that the average pore size of the Al2O3 sample is 7 nm, while that of the HZSM-5 sample is 0.5 nm. It can be seen that the apparatus gives results that are qualitatively correct. The quantitative measurement of the diffusivity was performed by the optimization of the parameter Dc in Eq. (1) using a visual comparison, that is, by looking at the computed curves corresponding to different values of Dc and deciding which one is nearest to the experimental curve. The pressure change versus time data reflect the diffusion times in the samples. By solving Eq. (1), we get the solutions and hence the diffusion times for different values of
Fig.2.Pressure change in the gas supply burette due to different samples.
1.26×108 (298 K) [8] 1.05×108 (298 K) [10] 7.0×109 (298 K) [1]
This work
2.0×109–4.3×109 (293 K)
diffusivity. These are then used to get the best match with the experimental data. The results are given in Table 1 and show that our apparatus can be used to measure diffusivities that are in the range shown in Table 1. An experimental difficulty is that there is a finite time interval at the beginning of the measurement when leak valve 6 is first opened. It was found experimentally that it takes about 10 s to get to and maintain a fairly constant final sample cell pressure. In Fig. 2, this 10 interval is the sharp increase in ǻp at the beginning left end of the curve. During this interval, much more of the (negative) ǻp in the gas supply burette is due to the supply of gas to increase the pressure in the sample cell (from zero pressure). In this region, since only a small fraction of ǻp is due to gas diffusing into the powder sample, diffusion data cannot be extracted and are “lost”. In the matching of simulation results and data, it is only data after t = 10 s that can be used. This places a limit on the magnitude of diffusivity that can be measured by the technique because this has to be sufficiently small or the particle made sufficiently large to give a diffusion time that should be > 50 s. This puts an upper measureable limit on the internal diffusivity of about 1×109 m2/s, with some possibility of going a little bit higher if larger particles are available. Fig. 3 shows a Monte Carlo (MC) simulation result that was optimized to match the experimental data from the methane-ZSM-5 diffusion experiment above. The MC simulation parameters include measurement uncertainties that were set as ± 0.5 °C for the temperatures of the gas supply burette, gas reservoir, and sample cell; ± 0.3% of the reading of the differential pressure of Baratron 5 (Fig. 1) if the reading was >0.2 torr, and ± 0.3% of 0.2 torr if the reading was 0.2 torr; ± 0.3% of the reading of the pressure of Baratron 9 (Fig. 1). The pressure in the sample cell was allowed to fluctuate within ± 3% of the pressure. After verifying that the MC simulation can fit the data, further simulations were carried out to seek ways to improve the apparatus. The simulation informs us that modifications should be made to the apparatus that can then allow measurements with a diffusing gas with a small Henry constant (K = 1) to be made. These modifications would use a smaller gas supply burette or/and a smaller sample cell, and the use of a 1 torr full scale Baratron. Also, the experiment should be planned with a slightly higher pressure in the gas supply burette than the pressure in the gas reservoir such that the ǻp of the gas
SONG Zhejian et al. / Chinese Journal of Catalysis, 2008, 29(11): 1133–1137
to the presence of micropores.
3 Conclusions The use of high precision differential pressure sensors provides a means to measure the internal diffusivity of microporous powders in a modified BET adsorption apparatus. This apparatus is cheap enough for even quite small laboratories.
References [1] Kärger J, Ruthven D M. Diffusion in Zeolites and Other Microporous Solids. Weinheim: Wiley, 1992. 1 [2] Kärger J, Ruthven D M. In: Schuth F, Sing K S W, Weitkamp J eds. Handbook of Porous Solids, Volume 4. Weinheim: WileyFig.3.Diffusion of CH4 in HZSM-5.
supply burette is close to zero for the experimental data used for parameter fitting. In working with microporous powders, e.g., as in measuring internal diffusivity here, a basic requirement of the apparatus is that it must be able to degas the very narrow pores. This is made possible in the present apparatus by the highly accurate measurement of the pressure and differential pressure changes. These have enough precision to allow the use of a large dead volume in the sample tube. This is necessary for working at very low pressures because a high pumping speed in the sample cell is required. Our apparatus ensures adequate pumping speed at the sample by using large tubings (8 mm inner diameter) to provide a fairly high conductance pumping path (hence, a large dead volume). In many apparatuses, the need to have a small dead volume requires the use of capillary tubings that limit the path conductance. These cannot give a high pumping speed at the sample that needs to be outgassed at very low pressures due
VCH, 2002. 2089 [3] Conner W C, Fraissard J. Fluid Transport in Nanoporous Materials. Heidelberg: Springer, 2006. 151 [4] Li W J, Wang Y, Wang D Zh, Wei F. Chin J Catal, 2006, 27(3): 200 [5] O’Sullivan C K, Guilbault G G. Biosens Bioelectron, 1999, 14(8–9): 663 [6] Qiao S Z, Bhatia S K. Microporous Mesoporous Mater, 2005, 86(1–3): 112 [7] Schuring D. Diffusion in Zeolites: Towards a Microscopic Understanding. Eindhoven: Eindhoven University of Technology, 2002. 13 [8] Goodbody S J, Watanabe K, MacGowan D, Walton J P R B, Quirke N. J Chem Soc, Faraday Trans, 1991, 87(13): 1951 [9] Keil F J, Hinderer J, Garayhi A R. Catal Today, 1999, 50(3–4): 637 [10] Caro J, Bulow M, Schirmer W, Kärger J, Heink W, Pfeifer H, Zdanov S P. J Chem Soc, Faraday Trans, 1985, 81(10): 2541